Question

If $a<0$ and $D<0$, then the graph of $y=a{x}^2+bx+c$
$(\text{where}D=b^2-4ac)$

• A. cuts the $x-$axis
• B. lies entirely below $x-$axis
• C. touches the $x-$axis
• D. lies entirely above $x-$axis

Answer 1

The correct option is B lies entirely below $x-$axis

For the equation
$y=a{x}^2+bx+c$
$a<0\Rightarrow$ downward opening parabola
Given
$b^2-4ac<0$
$\Rightarrow D<0\Rightarrow$ no real roots
The graph of $y=a{x}^2+bx+c$ lies entirely below the $x-$axis